Applications of PCF theory

DOI10.2307/2695067zbMath0981.03048arXivmath/9804155OpenAlexW2122408715MaRDI QIDQ2710599

Saharon Shelah

Publication date: 11 March 2002

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9804155

zbMATH Keywords

treeindependent setstable theorypcf theorycardinal invariantalmost disjoint familyregular ultrafiltertrue cofinalitydepth of a Boolean algebraultraproduct of Boolean algebrasultraproduct of cardinals

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20) Ordered sets and their cofinalities; pcf theory (03E04)

Related Items (12)

Interview With a Set Theorist ⋮ Forcing axioms for λ‐complete μ+$\mu ^+$‐c.c. ⋮ A note on edge colorings and trees ⋮ No universal in singular ⋮ The generalized continuum hypothesis revisited ⋮ Middle diamond ⋮ More on regular and decomposable ultrafilters in ZFC ⋮ On long increasing chains modulo flat ideals ⋮ More on the revised GCH and the black box ⋮ Towers and clubs ⋮ HIGHER MILLER FORCING MAY COLLAPSE CARDINALS ⋮ FREE GROUPS AND AUTOMORPHISM GROUPS OF INFINITE STRUCTURES

Cites Work

• Unnamed Item
• Chang's conjecture for \(\aleph_\omega\)
• On power of singular cardinals
• Reflecting stationary sets and successors of singular cardinals
• Set theory without choice: Not everything on cofinality is possible
• Further cardinal arithmetic
• Cardinal invariants above the continuum
• Special subsets of \(^{\text{cf}(\mu)}\mu\), Boolean algebras and Maharam measure algebras

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